Question

just paid a dividend of $1.60 per share. The company will increase its dividend by 20 percent next year and will then reduce its dividend growth rate by 5 percentage points per year until it reaches the industry average of 5 percent dividend growth, after which the company will keep a constant growth rate forever. If the required return on the company's stock is 17 percent, what will a share of stock sell for today

Answer 1

The share will sell for $16.31

Step-by-step explanation:

From the given information, the schedule of expected dividends is shown below:

Year Growth Dividend Calculation

0 1.6

1 20% 1.6(1.2) = 1.92

2 15% 1.6(1.2)(1.15) = 2.208

3 10% 1.6(1.2)(1.15)(1.1) = 2.4288

4 5% 1.6(1.2)(1.15)(1.1)(1.05) = 2.55024

5 5% 1.6(1.2)(1.15)(1.1)(1.05)(1.05) = 2.677752

Price of the stock today =
`(D1)/((1+ke)^1)+(D2)/((1+ke)^2)+(D3)/((1+ke)^3)+(D4)/((1+ke)^4)+(P4)/((1+ke)^4)`.

where P4 =
`(D5)/(ke-g)`

Price of the stock today =
`(1.92)/((1+0.17)^1)+(2.208)/((1+0.17)^2)+(2.4288)/((1+0.17)^3)+(2.55024)/((1+0.17)^4)+(2.677752)/((0.17-0.05)(1+0.17)^4)`= $16.31